HDU 4978 A simple probability problem.(概率模型+凸包周长)

#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const double epsi=1e-10;
const double pi=acos(-1.0);
const int maxn=10005;
struct point{
    double x,y;
    point(){}
    point(double xx,double yy):x(xx),y(yy){}
    point operator -(const point &op2)const{
        return point(x-op2.x,y-op2.y);
    }
    double operator ^(const point &op2) const{ //两个点向量的叉积
        return x*op2.y-y*op2.x;
    }
};
inline int sign(const double &x){
    if(x>epsi) return 1;
    if(x<-epsi) return -1;
    return 0;
}
inline double sqr(const double &x){
    return x*x;
}
inline double mul(const point &p0,const point &p1,const point &p2){
    return (p1-p0)^(p2-p0);
}
inline double dis2(const point &p0,const point &p1){
    return sqr(p0.x-p1.x)+sqr(p0.y-p1.y);
}
inline double dis(const point &p0,const point &p1){
    return sqrt(dis2(p0,p1));
}
int n,l;        //n个顶点，最近距离为l
point p[maxn],convex_hull;  //多边形顶点序列为p[],最低位置的点为convex_hull
inline bool cmp(const point &a,const point &b){ //相对最低点，各点极角从小到大，距离从近到远排序
    return sign(mul(convex_hull,a,b))>0||sign(mul(convex_hull,a,b))==0&&dis2(convex_hull,a)<dis2(convex_hull,b);
}
int convex(point *a,int n,point *b){ //计算含n个点的点集a的凸包b
    if(n<3) printf("Wrong in Line %d\n",__LINE__); //顶点数小于3，输出失败信息
    for(int i=1;i<n;i++)                          //计算最低点convex_hull
        if(sign(a[i].x-a[0].x)<0||sign(a[i].x-a[0].x)==0&&sign(a[i].y-a[0].y)<0)
        swap(a[0],a[i]);
    convex_hull=a[0];
    sort(a,a+n,cmp);                      //按极角和距离排序
    int newn=2;
    b[0]=a[0];b[1]=a[1];                //a[0],a[1]入栈
    for(int i=2;i<n;i++){
        while(newn>1&&sign(mul(b[newn-1],b[newn-2],a[i]))>=0) --newn; //弹出栈顶所有未左转指向扫描顶点i的元素
        b[newn++]=a[i];                   //顶点i入栈
    }
    return newn;           //栈顶指针
}
int main(){
    int t,cas;
    scanf("%d",&t);
    for(cas=1;cas<=t;cas++)
    {
        scanf("%d%d",&n,&l);
        for(int i=0;i<n;i++)
            scanf("%lf%lf",&p[i].x,&p[i].y);
        printf("Case #%d: ",cas);
        if(n>2)
        {
            n=convex(p,n,p);
            p[n]=p[0]; //首尾相连
            double ans=0;
            for(int i=0;i<n;i++)
                ans+=dis(p[i],p[i+1]);  //累计凸包边长
            //ans+=2*pi*l;
            printf("%.4lf\n",ans/(pi*l));
        }
        else if(n==2)
        {
            double ans=dis(p[0],p[1]);
            printf("%.4lf\n",2*ans/(pi*l));
        }
        else
            printf("0.0000\n");

    }
    return 0;
}